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Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 19–34 | Cite as

When a line graph associated to annihilating-ideal graph of a lattice is planar or projective

  • Atossa Parsapour
  • Khadijeh Ahmad Javaheri
Article

Abstract

Let (L,∧, ∨) be a finite lattice with a least element 0. AG(L) is an annihilating-ideal graph of L in which the vertex set is the set of all nontrivial ideals of L, and two distinct vertices I and J are adjacent if and only if IJ = 0. We completely characterize all finite lattices L whose line graph associated to an annihilating-ideal graph, denoted by L(AG(L)), is a planar or projective graph.

Keywords

annihilating-ideal graph lattice line graph planar graph projective graph 

MSC 2010

05C75 05C10 06B10 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Department of MathematicsBandar Abbas Branch, Islamic Azad UniversityBandar AbbasIran

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